Generation of Multistability through Unstable Systems

Abstract

The main aim of this paper is to generate multistability from a type of unstable systems which have all their roots in the right half of the complex plane. For the realization of this, we use a system of linear differential equations that consists of two parameters. First we use an instability parameter to transform an unstable system to a type of system capable of generating attractors by means of a piecewise linear function. Then we use another bifurcation parameter to change from multiscroll attractors in a mono-stable state into several single-scroll atractors in multi-stable states.